addpath ../../../../CEtools64/


load eq_mit_mass.mat
eq_mit_kimball = eq_mit;
clear eq_mit;


mit_flag = 4;

%% Set Options
% All
options.Nbell       = 100;        % Number of Bellman iterations before Newton.
options.Nnewt       = 15;       % Maximum number of Newton steps
options.tolc        = 1e-12;     % Tol on value functions
options.T_irf       = 50;       % Number of periods for IRFs
options.T           = 300;     % Number of periods for MIT shock
options.Terg        = 500;      % Number of periods to burn
options.hpisteps    = 100;

% Stationary
options.L = [];
options.itermaxL    = 5000;     % Max number of iterations to find L
options.tolL        = 1e-12;    % Tol for L
options.tolK        = 1e-5;     % Tol for equilibrium K
options.itermaxK    = 100;      % Max iterations for bisection
options.cresult = [];

options.tolD        = 1e-08;
options.itermaxp    = 25;

options.damp = 0;
options.damp_mit = .8;
options.damp_DC  = .9;

optset('bisect', 'tol', 1e-12)

%% Set globals and parameters
% % try vavra numbers
glob.n          = [100,30];   % Number of nodes for b,a
glob.nf         = [100,30];

glob.spliorder  = [1,1];    % Order of splines (Envelope Condition Method seems only robust when quadratic in k)
glob.Na         = 30;           % Number of nodes for quadrature
glob.curv       = .1;            % Amount of curvature for p grid

glob.Nsignal    = 1e6;

glob.minb = 1e-5;
glob.maxb = 20;


%% Model parameters

% preferences
param.beta      = 0.96;               
param.mu_s = 0;

%  rho_s    phi_L  sigma epsilon   ce_mu     d_E
% 0.60338 0.076289 2.9199   2.835 -2.3445 0.59226

% idiosyncratic shock - set 'em and forget 'em

% note - berger just chooses rho - .81 and sigma = .38 (annual)

%%%%%%%%%%%%% CALIBRATE HERE %%%%%%%%%%%%%
param.sigma_s         = 0.18; % concentration & variance
param.rho_s           = 0.79;  % Concentration & variance
 
% labor adjustment cost
param.phi_L           = 0.07; % as a start, no adjustment costs
 
% Demand parameters
param.sigma           = 20;              % FIX THIS NUMBER, let go of average markup
param.epsilon         = .6*param.sigma;     % epsilon/sigma is superelasticity, 0 is CES 
 
% fixed cost of production
param.mu_f     = -1e6; 2.15;
param.sigma_f  = 1.65;
 
% dist of entrant productivity signals
param.xi     = .95;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

param.omega           = 1;                  
         
param.A = 1;

% entry and exit
param.gamma = .11;     % exogenous exit rate

% sunk cost of entry 
param.ce       = exp(-1);exp(param.mu_f + param.sigma_f^2/2);
param.ce_noise = 1e-3;

param.M        = 1;


param.nu      = .5; % inverse Frisch elasticity
                     % same as in clementi
                     % can calibrate aggregate shock size to hit moments

% free labor adjustment 
param.delta    = 0.19;

glob.mink       = 0;


%% Find initial steady state
options.itermax_DC = 100000;

superelasticities = [.54 .56 .58 .6 .62 .64 .66];
for i = 1:length(superelasticities)

    se = superelasticities(i);
    
    param.sigma           = 20;              % average elasticity
    param.epsilon         = se*param.sigma;     % epsilon/sigma is superelasticity, 0 is CES 
    glob.maxk       = param.sigma^(param.sigma/param.epsilon);

    
    [param,glob]    = setup(param,glob,options);

    eq_SS           = solve_eq_ss(param, glob, options);
    % param.mu_entry  = eq_SS.mu_entry;
    % param.mu_f      = param.mu_entry - param.mu_f_diff*abs(param.mu_entry);

    glob.agg = kimball_agg(1, eq_SS, param, glob); % Fix this value!
    L        = sum(eq_SS.l.*eq_SS.L);
    param.psi = 1/(L^param.nu); % psi = 1/(L^nu*C)

    % check that C = 1... 
    tosolve = @(C) kimball_agg(C, eq_SS, param, glob) - glob.agg;

    fprintf('C is %.5f \n', bisect(tosolve, .5, 1.5));

    % %% nvm
    % calib = [0.093017 10.753 1.7897 -5.0936  1.1223 2.196 0.62235];
    % mom = compute_moments_for_calibration(calib, param, glob, options);

    %%
    mom = compute_moments(eq_SS, param, glob, options);
    beta_l(i) = mom.beta_l;
end

%%
close all

plot(superelasticities, beta_l,'LineWidth',4)

title('')
xlabel('Super-elasticity')
ylabel('Within Firm Labor-Sales Regression')

set(gcf,'units','points','position',[10,10,500,300])
set(findall(gcf,'-property','FontSize'),'FontSize',16)

print('-dpng', 'figures/superelasticity_identification.png')
